Spectral stochastic modeling of uncertainties in nonlinear diffusion problems of moisture transfer in wood

Abstract

This paper deals with the stochastic numerical analysis of moisture transfer in wood with the random diffusion coefficient after heating of wood (when temperature is already constant). The simulation is based on the unsteady-state nonlinear (the model respects the dependence of diffusion coefficients on moisture and constant temperature) diffusion of moisture with respect to the orthotropic nature of wood. The spectral solution of this problem is based on discretization the resulting random field (moisture) in the stochastic dimension by the orthogonal polynomials (generalized polynomial chaos algorithm). A Galerkin projection is applied in the stochastic dimension to obtain the deterministic set of partial differential equations that is solved by finite element method.The main purpose of this paper is to demonstrate that the stochastic spectral method based on polynomial chaos expansion can be more efficient in modeling uncertainties associated with moisture transfer in wood than Monte Carlo method mainly when considering a small number of random variables. This spectral approach has a big advantage over the Monte Carlo method (statistical approach) in terms of computer time. Numerical example of diffusion of moisture in convective drying of wood is given and there is shown that the results (mean and the standard deviation) obtained with the stochastic spectral method are in good agreement with the results of the Monte Carlo simulations.